# Mathematical and Statistical Methods in Biology (2018/2019) Course code
4S004794
Credits
6
Coordinator
Giacomo Albi
BIO/13 - EXPERIMENTAL BIOLOGY
Language of instruction
Italian
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
Parte 1 3 I semestre Giacomo Albi

Parte 2 3 I semestre Roberto Chignola

### Learning outcomes

The course is an introduction to the basic and most known mathematical models developed to solve biological and medical problems.
We will discuss deterministic as well as probabilistic models, together with the statistical tools used to quantify the uncertainties characterizing complex biological systems.
At the end of the course the students should be able to :
- understand and discuss the main models of biological systems, with particular attention to the validity of the assumptions, and the definition of different parameters;
- develop and analyze simple models;
- understand the impact of the parameter, also with respect to their measure uncertainty;
- compare the predictions of the models with the experimental data;
- communicate the results in an interdisciplinary environment.

### Syllabus

Part I (Albi)

A) Discrete, and continuous model of single population:
* Growth models
* Time delay models
* Biological systems with feedback
B) Discrete, and continuous model of interacting populations
* Linear and non-linear models: Predator-Prey models; SIS, SIR models, tumor growth.
* Single perturbed systems & oscillators: Enzyme Kinetics, Fitzhugh–Nagumo Model for neuronal membrane,
synchronization models.
C) Discrete and continuous probabilistic models:
* Stochastic growth models, and stochastic predator-prey models, oscillators with random noise.
* Reaction-Diffusion processes, Chemotaxis.
* Monte-Carlo methods
D) Parameter identification and data analysis
* Statistical inference, theory of the estimators, maximum likelihood, test of hypothesis.
* Data fitting, Linear and non-linear regression, Kalmann filter, sensitivity analysis.

Part II (Chignola)
- probabilistic models for biomedicine
- the Luria and Delbrück experiment
- growth models for population biology
- allometry and scaling laws
- phenomenological models for tumor growth
- models for cell physiology
- multi-scale models in oncology

### Assessment methods and criteria

Part A: written exam with the help of computer, solution of exercises on the basis of the one solved during the course. Students will be required to modify the numerical codes seen in Matlab/Octave. Possibility of midterm examination.

Part B: Oral evaluation. The students will have to prepare and critically discuss a short essay.

 Activity Author Title Publisher Year ISBN Note Parte 1 J. Murray Mathematical Biology Springer 2002 0-387-95223-3 Parte 1 J. D. Logan, W. R. Wolesensky Mathematical Methods in Biology 2009 9780470525876 Parte 1 Brian Ingalls Mathematical Modelling in Systems Biology: An Introduction Parte 1 V. Comincioli METODI NUMERICI E STATISTICI PER LE SCIENZE APPLICATE Universitá degli Studi di Pavia 2004